This eighth grade mathematics lesson focuses on the application of the Pythagorean Theorem, raising expressions to certain powers, and operations with algebraic expressions. It is the second lesson in a unit of work focused on algebraic expressions. The lesson is 45 minutes in duration. The lesson was taped in a gymnasium - a school that specializes in preparing students for university. There are 30 students in the class.

00:00:04Dan, Dan stop it. So, Stephanie came back, and Hanka is still absent. Any other changes?
00:00:21Good, then today we will start with Pythagorean theorem. Get ready, take your notebook and write today's date, number of the class.
00:00:38So, the number of the class is 30, today's date. So, I'm going to invite up here Marcela Draslerova, come on Marcela.
00:01:00So, Marcela write the problem statement on the board. I would like you to calculate. We have a given rhombus, which has two diagonals.
00:01:15One is 12 centimeters long, the second one seven centimeters. So please Marcela, find out the perimeter of the rhombus. What is the perimeter of this rhombus?
00:01:37Do you need me to turn the light on? Is it better? So Marcela, talk.
00:02:13So, Marcela, explain.
00:02:16So, diagonals are split into halves, with the help of the Pythagorean theorem we'll figure out the length of each side.
00:02:26Sides. Marcela, what kind of shape is it? The rhombus. The attribute of the diagonals you've explained, one point is discovered, is there any other?
00:02:35It's (inaudible).
00:02:37Yes, that too, we would certainly need it.
00:02:42Psst, Dan!
00:02:43Oh, yes. It has all the sides the same.
00:02:44So, I'm not going to count that, because it was heard before here. So, all the sides are the same length, in that case, we can make the picture easier.
00:02:55There, yes.
00:03:18So, Marcela, I'm going to ask you. You've said, you are going to work with it in a right triangle. How do you know, that triangle is right-angled?
00:03:25Specify there, in which one you'd like to work with the problem. One of them, whichever you choose.
00:03:29So, how do you explain or how do you convince us, that this triangle-
00:03:32Because the diagonals are perpendicular to each other.
00:03:35So, you didn't say that before, yes that's correct.
00:03:48So, Marcela, speak out loud so everybody knows what you're writing on the board.
00:03:50Plus (inaudible) divided by two.
00:03:57A is equal to the second root of 12 divided by two and square the whole formula, plus seven divided by two and square the second formula.
00:04:15So, when you substitute.
00:04:17A is equal to second root of six square.
00:04:27Uh huh.
00:04:28Plus (inaudible), plus three point five.
00:04:50So, here is the calculator, Marcela.
00:05:04What is it?
00:05:05Twelve point twenty-five.
00:05:06Twelve point twenty-five.
00:05:31Six point, six point eight.
00:05:37Is it rounded to something? So, did you enter it in the calculator correctly, Marcela? What did the calculator show you?
00:05:42Six point eight (inaudible) nine four.
00:05:44Okay, okay, so it's six point, you said eight?
00:05:46Oh, yes. It's six point nine.
00:05:47Good, of what?
00:05:53Centimeters. Yes, yes. Move a little to the side, Marcela. So, look at the first procedure.
00:05:58Do you have the same results? Any problems so far?
00:06:00So, Marcela, what else?
00:06:02(inaudible) is equal.
00:06:04Uh huh.
00:06:18Marcela, six point nine by, yes, four.
00:06:27So, we'll try it without a calculator, what would it be.
00:06:40It is twenty-seven point six.
00:06:43Yes, it's twenty-seven point six.
00:06:50Okay, Marcela, it was correct, go sit down. So, do you all have the same answer?
00:06:55Did anyone have a problem? So, Marcela, it's going to be B for you today, because of the basic figure, because the rhombus was not exactly pictured out.
00:07:02And, unfortunately, we cannot count it, because of Dan's suggestion, so Marcela is going to get B.
00:07:09So, let's try the second time, and it would be for Dan. Let's go Dan.
00:07:19So, Dan, I'd like you to calculate. Do you have a chalk? Calculate the length of the diagonal of the parallelepiped.
00:07:30So, write over there, that it's a parallelepiped.
00:07:37So, calculate the length of the body diagonal, when the measurements of the parallelepiped are: three point two decimeters.
00:07:47The second measurement is 46 centimeters, and the third measurement is going to be five point three decimeters.
00:08:00So, what kind of adjustment did you make? Already, yourself?
00:08:02I transferred it.
00:08:03Transferred to centimeters. So, Dan. I'd like to calculate the length of diagonal of this parallelepiped.
00:08:15So, I'm going to make a sketch.
00:08:16So, let's start with a sketch.
00:08:23A diagonal.
00:08:25I'll inscribe the sides of the parallelepiped (inaudible).
00:08:36And you have to speak out loud so they can hear you all the way here in the back.
00:08:39(inaudible) A (inaudible) B (inaudible) C.
00:08:43And Dan, in this parallelepiped they are not sides, but-
00:08:47The edges, yes.
00:08:48The edges.
00:08:49Now, I'm going to calculate the side A G.
00:08:52A G.
00:08:55Is it going to be the length of the diagonal? Yes. Mark it into the sketch.
00:09:06And now it's up to you how we're going to calculate it.
00:09:13So, we will separate it on one side to A, B, C and we'll mark it as a right-angled triangle.
00:09:21So, you meant a wall not a side, a wall yes, so walls A, B, C and D we can use.
00:09:22A wall.
00:09:24(inaudible) walls A, B, C, D, (inaudible) a short diagonal to the right.
00:09:37Uh, huh, yes, mark the right angle there, so it's clear.
00:09:44And loud, Dan, you have to speak out loud so we can understand what you're saying.
00:09:46So, these are (inaudible) A (inaudible) B and this is going to be a diagonal, let's call it for example X.
00:09:52So now we can easily figure it out, so X equals a root of A squared plus B squared because it's a hypotenuse.
00:10:03So X equals a root of 32 squared plus 46 squared.
00:10:12Uh huh.
00:10:16So, Dan, take your calculator or over there on the table you can borrow one.
00:10:28So, I'll write it down. It's a root of 1,024 plus 2,016.
00:10:41Uh huh.
00:10:44I'll add it together, so it's a root of 3,140.
00:10:57And the result is 56.
00:10:59Uh huh, centimeters, good. So, by doing this we calculated what?
00:11:05A wall diagonal.
00:11:08The length of the wall diagonal. Okay, what is next?
00:11:10Now (inaudible).
00:11:13So, now we get a right-angled triangle A C G.
00:11:17Yes, so draw the triangle again.
00:11:26This is going to be A, this is C and this is G and this is going to be (inaudible) Y.
00:11:38So you said that the triangle is, Dan, right-angled. So, this is clear.
00:11:44So, this is practically the (inaudible) C, and this the wall diagonal X and we have to calculate the Y.
00:11:54So, Y is equal- because it's a hypotenuse- it's a root of X squared plus C squared.
00:12:05So Y is equal to the root of 56 squared plus 53 squared, and Y is equal, where is the calculator.
00:12:13Uh huh.
00:12:18So, you borrow this calculator again.
00:12:29So, it's the root of 3,136 plus 2,809, Y equals the root of 5,945.
00:12:49Uh huh.
00:13:01And that is seventy-seven point one, seventy-seven point one centimeters.
00:13:11Yes, Dan, that was correct. So, now the rest of you take a look at it, Dan was just mumbling over here by the blackboard.
00:13:16So you look at it if you have the same answer.
00:13:19So, Dan, before I let you go tell me how many decimeters it would be.
00:13:22Seven point seventy-one decimeters.
00:13:24That's correct, thank you. So, what about the rest of you. Do you have it or anyone found a problem? Is it good?
00:13:31So, Dan is going to get A today.
00:13:34It was without any mistakes. Now it's an assignment for all of you. I'd like you to do this third part each by yourself.
00:13:45Are you finished? May I start?
00:13:48So, write in your notebook: an easel has sides two point five meters long, an easel has two sides two point five meters long.
00:14:03Everybody knows what an easel looks like? Everybody has seen an easel?
00:14:05Two point what?
00:14:07So, an easel has sides two point five meters long. Calculate, calculate, how far, calculate how far they reach, calculate how far they reach.
00:14:27If the ends of the sides touching the ground, if the ends of the sides touching the ground are one point five meters apart from each other.
00:14:43If the ends of the sides touching the ground are one point five meters apart from each other.
00:14:56So, one more time and slowly. We have an easel, they have sides two point five meters long.
00:15:02I'd like to calculate how far they reach, when you know, that the sides are reaching the ground and the two points are one point five meters apart.
00:15:14Everybody knows what an easel looks like? Can you imagine a picture? Katka?
00:15:17Right-angled (inaudible). Right-angled (inaudible).
00:15:20It depends how you mark it for yourself. It's up to you. Make a sketch, mark sides by your choice.
00:15:27Calculate, how far we can climb, when we're going to stand on the top of the easel?
00:16:25And always in your sketch, don't forget to mark what triangle you are using for calculating.
00:16:30And, also realize what each side of the triangle means.
00:16:59So, who's ready? How are we doing?
00:17:09So, it's just George, nobody else? Somebody has the answer? Tomas with George.
00:17:22So, Tomas. Come up here and write it down.
00:17:27Take your notebook with you and get it ready in the back of the blackboard, so we can check it faster.
00:17:32Hide yourself back there, so you don't give a hint to others. Okay, let's hide you over there, and I'll close it behind you.
00:17:51So, who has any answer raise your hand. I'd like to see it before Tomas finishes it up and we'll look at it together. Yes, that's correct.
00:18:00You need to clarify the measurement. Yes, Marcela rounded the total. Yes. Yes.
00:18:07Kamila, what is it? Uh huh, yes. George? Yes. Martina? Yes.
00:18:20You jumped a little too much. Check it out again, Marcela and correct it. You have some kind of numeric mistake there. Look at it.
00:18:26So, where didn't I go so far? Yes. Dan. Yes, Jonas. Do you have anything written? Good.
00:18:33I have already.
00:18:34So, who's work haven't I seen? Yes. Yes. Who else? So, Tom, what does it look like back there? Are you done? Can we look at it?
00:18:43So, round it up, Teresa, but yes, it's correct. Yes, that's right. So, where didn't I go? Dado, show me your work. Yes. Yes. Good.
00:18:55So, Tomas, can we take a look? So, I checked out most of your work.
00:19:15So, good Tom, you can sit down. So we have one option how to calculate this assignment. Look at it. Pss. Quiet.
00:19:24And, check it out if you have the same result, or you came up with any other procedure.
00:19:31Does anyone else have another procedure? And what about the result? Is it the same?
00:19:37So, when I walked around, I found more or less correct answers.
00:19:40We agreed, we're going to have the measurements with one decimal space, so we'll round the answer on two decimal spaces.
00:19:46On two.
00:19:47Somewhere I saw it rounded up to two point four, someone else had it more specific. It really doesn't matter.
00:19:52Most of the time, we'll leave it rounded to two decimal points. So, there was no problem and we all got it.
00:19:56Good, so now I want you to take your homework and we'll go through numeric terms in your homework.
00:20:09So, get ready.
00:20:16So, can we start? Did you find it in your notebooks? So each of you will do one example and we'll go through it really fast and make it right.
00:20:21So, Marcela, you start.
00:20:22Four plus three times two squared, is four plus three times two and that is 16.
00:20:27That is 16. If there is any problem, tell me right away. Zuzko!
00:20:32Four plus three times two squared, that equals four plus six squared is equal to 40.
00:20:39Yes, that is 40, Dan.
00:20:40Four plus three, in parenthesis, times two squared is equal to seven times two squared and that is 28.
00:20:48And that equals 28. Excellent. Petra.
00:20:51Four plus three times two in parenthesis raised to the second power is equal to 100.
00:20:55Is 100. Petra did it very fast. Katka.
00:20:59Four minus three times two squared is equal to four minus 12 and that is minus eight.
00:21:03And that is minus eight. Katka. Take another one.
00:21:06Four minus three times two squared is equal to four minus six squared and that is minus 32.
00:21:13Minus 32. Jonas.
00:21:15Four minus three in parenthesis times two squared is equal to one times four is four.
00:21:21Is equal to four. Martina.
00:21:23Four minus three times two in parenthesis squared is equal to four minus six all raised to the second power and that equals four.
00:21:31And that is four. So, is everything okay? Did you have any problems? Good.
00:21:35So these are numeric terms and I would like to review a few more complicated ones, when there is something more complicated, if not, we'll come up with something.
00:21:44So, we'll start on page 100 in your textbook and I'd like you to figure out the shown assignment two, and we'll also do the example E.
00:21:57And, who's going to be finished before we'll finish on the blackboard.
00:21:59So the next one you can think about is on page 104, problem number four.
00:22:06And that one we'll do from the beginning to the end.
00:22:07So, first we'll start with the E example. Everybody will calculate one example on the blackboard.
00:22:11This week's service person will in the meantime clean what we've already written on the blackboard.
00:22:15And let's go. Each of you, let's do one piece. And Jana's going to start. Come on Jana.
00:22:24So, Jana, five plus three in the parenthesis divided by four squared, yes the end of parenthesis and divided by four squared.
00:22:37So, Jana, talk and explain what you're doing there.
00:22:38So, the parenthesis come first, so it's eight divided by, four by four is 16, is eight divided by 16 minus two.
00:23:05Are you sure Jana? Eight divided by 16. We're dividing eight by 16.
00:23:21What is it? What is it? Jonas?
00:23:22Zero point five.
00:23:23Zero point five, Jana. Be careful, it's the other way around. So, why do you think it should be minus? Where would you get the minus?
00:23:30I don't know.
00:23:31So, there is no minus. Or, anyone has the answer in a different form?
00:23:35One half.
00:23:36One half, of course. So, Jonas, let's do another one. So, you don't have to take your textbook, you just do it.
00:23:42Five minus three divided by the second root of four.
00:23:50So, the root of four is two, three divided, so five.
00:23:56Uh huh.
00:24:00So, don't forget it's equal, at the beginning make another one, at the beginning, at the beginning, so.
00:24:06Three divided by two is one point five, five minus one point five is three point five.
00:24:15Three point five, uh huh. What about you? Do you agree with that? Nobody has a problem. So, let's do another one.
00:24:22So, Jirka Kral is going to take the next one. Come on Jirka.
00:24:28So, Jirka, for you we have five plus, and in the parenthesis three divided by four, the parenthesis squared.
00:24:36So, it's five plus, uh, three divided by four is zero point, uh.
00:24:47Yes, that is coming, let him be, let him be.
00:24:51Seventy-five, 75.
00:24:54It looks a little weird.
00:24:57So. Now you tell me, what you're going to do next with the formula when you should raise by two.
00:25:02So, I'm going to raise it by two.
00:25:06Similar to the easel.
00:25:07So, Jirka, now calculators are prohibited, I need you to think about it without calculators. How are you going to do it without a calculator?
00:25:13Shh, shh stop that.
00:25:14Well, we'll draw it.
00:25:18No, no, we'll just calculate today not draw.
00:25:23That's because the zero point 75 is not the best form, Jirka.
00:25:27Go back, go back to the three fractioned by four, three divided by four, okay so now I've said that.
00:25:35So, yes. So without a calculator we'll try it now.
00:25:45Yes, so. And now we'll know what to do.
00:25:59So, I want you to write it in the form of a single fraction, Jirka. What is this form called?
00:26:04This is a complex fraction.
00:26:06This isn't a complex fraction. How is it called?
00:26:09Mixed number, and now I'd like a simple fraction.
00:26:19So, in this form for example, good Jirka. So, do you all have it? Can we do another one? So, Teresa, come to do another one.
00:26:27But when we had the easel we did it differently.
00:26:29Yes, we could have. Yes. So, Teresa, we have for you five minus three in parenthesis, divided by the square root of four and all raised to the second power.
00:26:42Entirely the whole thing, squared.
00:26:50Five minus three is two, divided by the root of four is two and the whole formula squared.
00:27:00So, it's two divided by two, that is one squared, and that is equal.
00:27:04Which is equal?
00:27:05One, that's correct. So, do we all have it? Any problems?
00:27:09So, now I want you to, everyone on your own solve the problem in example number four.
00:27:16What do we have to do there, Martina? Read it.
00:27:18Fill in the blanks the correct answers of signs for bigger and smaller.
00:27:22Bigger, smaller. So, calculate and fill out the correct answer bigger than, smaller than, equal.
00:27:29So, without calculators, without calculators, Petra, your brain needs to work.
00:27:43Martina, Martina, don't sleep. Do you have it? Awesome.
00:28:00So, write down also the answers between, so we can check it out and we can explain why it is that way, not just having the answer written down.
00:28:35So, finish writing and calculating.
00:28:53Dan, look into your notebook, not elsewhere.
00:28:59So, shall we. Raise your hand how we're doing, who's already done? So, one more second and finish writing.
00:29:12So, let's check it out. So, always read the problem statement, tell me the between answers so we're sure that it's correct and check, if your answers are the same.
00:29:20So, Dada, do the first one.
00:29:22So, it's two squared plus two squared is equal to two times two squared, so two squared plus two squared is eight.
00:29:31And two by two squared is also eight.
00:29:34Yes. So in the A example the answer was equal. Petra.
00:29:37Two squared plus two cubed, oh, I have to do example B, two cubed plus two cubed, is bigger than three times two squared.
00:29:42It doesn't matter
00:29:47Because the cube of two plus the cube of two is 18.
00:29:52So, how much is the cube of two, Petra?
00:29:53The cube of two is eight.
00:29:54Eight, so on the left side the answer is 16 and on the right side?
00:29:58And three by two squared is 12.
00:30:01Twelve, so.
00:30:02So the 16 is bigger than 12.
00:30:04The left side is bigger than the right one, Jitka.
00:30:07So, two squared plus two cubed is equal to three by two squared.
00:30:12So, what did you get on the left side?
00:30:13So, it's basically four plus eight which is 12 and three by four is also 12.
00:30:21So, in example C we have, say it one more time an equal symbol, good, Karin, take another one.
00:30:23An equal symbol.
00:30:26Two cubed plus two squared will be eight plus four.
00:30:28Jirka, stop doing that.
00:30:31Which is 12 and that is smaller than two times two cubed, because it's like two times eight, 16.
00:30:35Which is?
00:30:36Sixteen, so, we all have it, we all know it. So, now I have something more difficult for you.
00:30:41Open your textbook on page 103.
00:30:45Until now you've had the expressions given, so now we're going to try it the other way around.
00:30:48On page 103 it's shown at the beginning how you can translate this numeric expression into words.
00:30:58Let's try it if it's more difficult and we'll express it in words. So, the beginning is very simple.
00:31:04The sum of numbers three and five we'll convert into words how?
00:31:09Three plus five.
00:31:10Three plus five. The difference between numbers four and minus eight?
00:31:15Four minus minus eight. The product means what, Misa?
00:31:23Multiplying, or by. And quotient?
00:31:24Dividing, so these are the basic functions and of course, that's not enough and unfortunately we'll have more difficult ones.
00:31:29So, now we have the more difficult ones here. So, now approximately in the middle of the page look and we have some expressions.
00:31:35And there are also powers and roots. So, now we're going to try to read this example and later on we're going to think about it on our own.
00:31:41So, Andrea, try the first one.
00:31:44A four power of difference of numbers five and three.
00:31:47Now, look next to it how they wrote it down.
00:31:50Five minus three in the parenthesis to the fourth power.
00:31:52So, how do we do it that we have the same process as always? So if we're going to calculate it what do we have to do first?
00:31:59Put it in the parenthesis.
00:32:01First, we have to do the calculation in parenthesis and after that raise it to a certain power.
00:32:03Parenthesis and raise it to a certain power.
00:32:06So it's called the fourth power and after that we talk about the difference.
00:32:12So, what kind of calculating am I starting with in this word expression?
00:32:16With the power.
00:32:18With the power, which means, with the process which we're going to be using for calculating as the last one.
00:32:22The last one.
00:32:24First we have to subtract and when we have the answer, we'll raise it to a certain power, okay?
00:32:27Raise it to a certain power.
00:32:29So, let's try the second one. Be careful so you don't have chaos in it. Teresa.
00:32:35The difference of fourth powers of numbers five and three.
00:32:39So, what are we going to start with? First we should calculate what?
00:32:46First we're going to calculate the fourth power.
00:32:48First we're going to calculate the fourth powers and later the answers we'll subtract.
00:32:51We'll subtract.
00:32:52So, look at the word expressions and it starts with "the difference of fourth power". Do you understand that?
00:33:00Okay, so let's try another one. Lucko, read the next one.
00:33:03Five multiplied by the sum of the numbers 12 and three.
00:33:04So, if we want to calculate it, first we start with what?
00:33:11First we calculate the parenthesis which is 12 plus three.
00:33:13Twelve plus three and the answer, we multiply it by five.
00:33:16Multiply by five.
00:33:17Look at it how it starts. It's five multiplied by a certain sum.
00:33:21So let's try the last two ones. They are going to be the most difficult ones, because we haven't practiced them yet.
00:33:27Let's try them, Kamco. The one before the last one.
00:33:30The square root of the sum of 11 and seven.
00:33:33And now we'll read the last one so you have something to compare it to, Pepo, what is going to be the last one?
00:33:38The total sum of square roots of numbers 11 and seven.
00:33:40So, now look at it how it's written. When I start saying: second root of the total, so the main part is the big root mark.
00:33:50The root mark.
00:33:51And in the last one you have the sum of the square roots.
00:33:54Square roots.
00:33:55So, be very careful, because it's a play with words how you formulate it and it's up to that how you write it down.
00:34:01So, did you understand that? So, I have prepared an easier version for the beginning and I hope it's going to be fast.
00:34:08Now pass it around to each desk, you'll get one example.
00:34:20You'll be able to do it on your own.
00:34:26So it's not just I want you to write it, I also want you to calculate it. So, let's do the example number three as a first one.
00:34:36So, write it down and at the same time calculate it. So far just the example number three.
00:34:41Go through it, go through it, write it down and calculate it.
00:34:46So, I hope there are not going to be any problems with powers and roots, we'll start with the easier ones.
00:35:40So get the number three ready at this point, we'll check it out and after that we'll go further.
00:36:02Read it very carefully so you don't make a mistake. It's better to read it two times before you write it down.
00:36:23So, how is it going? Who has everything? So, a little longer.
00:37:04So, let's do it. So, always read what you've written down and after that, what the answer is. Katko?
00:37:11The difference of numbers 15 and nine is 15 minus nine is six.
00:37:14And the answer is?
00:37:15It's equal to six. Marketa!
00:37:17Fifteen times nine is 135 and it's a product of numbers 15 and nine.
00:37:20One hundred and thirty...
00:37:21You don't have to read it because you all have it there. So, Dan, read the next one.
00:37:25Sixty-four divided by eight is eight.
00:37:27Sixty-four divided by eight is eight. Karin!
00:37:30Seventeen plus 12 is 29.
00:37:32Twenty-nine. Alino.
00:37:34Fifteen plus two times nine is 33.
00:37:37So, what comes first? Don't forget about it, let's remember it.
00:37:41The multiplication.
00:37:42The multiplication. So, let's do the next one. Jitko!
00:37:46In parenthesis 15 plus nine, the end of parenthesis, times four is equal to 96.
00:37:49Times four.
00:37:51It's 96. Dado!
00:37:53Two times 15 plus nine in parenthesis, plus two times 15 plus nine in parenthesis.
00:38:00So what is the answer?
00:38:02Are the parenthesis necessary there, or we can get by without them?
00:38:06We have to have them.
00:38:08Yes, we have to have the parenthesis here, so let's move on, Katka.
00:38:11May I ask something?
00:38:13About the multiplying by two. Does it matter if it's in front of or after the parenthesis?
00:38:17So, Katko, show me what we have here.
00:38:18If I look at the answer it doesn't matter, but it's written differently.
00:38:22So tell me what you have there.
00:38:23Fifteen plus nine in parenthesis by two.
00:38:28So, it's this way or what kind of different version did you want?
00:38:30Two by the whole parenthesis.
00:38:34The answer is the same, but if I write it the other way, is there any difference?
00:38:39How do we explain that the answer has to be the same no matter what way we write it down?
00:38:42Because it's commutative.
00:38:43Multiplying is commutative.
00:38:44It's commutative.
00:38:46Sure, so, where are we? So we have also the last one. Zuzko!
00:38:51Fifteen times two plus nine times two is equal to 48.
00:38:54So, Zuzko, are the parenthesis necessary there? We can do it without and the answer is 48.
00:38:55So this first example was hopefully easy. Without a problem.
00:39:02So now I'd like you to try something with decimal numbers possibly something with fractions, so let's try problem number 10.
00:39:18So, now we can start. You try it by yourselves first and on the blackboard you'll have it for comparison.
00:39:19So, we're going to write it on the blackboard. We'll choose always a couple if we have enough space.
00:39:22First we start with two people and it's going to be Marcela and Micha. Come on girls.
00:39:29I'll try to dictate it for you first. So you should just hear it not see it, and try to write it down.
00:39:34So, it's the product of numbers four and 11 made bigger by the difference of numbers 100 and 37.
00:39:49Made bigger by the difference of numbers 100 and 37.
00:39:53So, I'll read it one more time girls. Listen to it and check it.
00:39:56The product of numbers four and 11 made bigger by the difference of numbers 100 and 37.
00:40:04Marcelo, I started with the product of numbers four and 11. Yes. So, finish calculating.
00:40:26So, girls, you can sit down now. Did you get the same answer?
00:40:30So now we'll try a couple of boys. Jirka with Pepa for example, come on boys.
00:40:38So boys, we made this up for you.
00:40:41From the sum of numbers two point four and five point six, from the sum of numbers two point four and five point six we'll subtract, subtract.
00:40:54The quotient of numbers 42 and six. We'll subtract the quotient of numbers 42 and six.
00:41:04Yes, so you started the right way. Finish calculating it.
00:41:20You can go and sit down now guys. So check it. I'm also going to ask.
00:41:24Look at the blackboard. Pepa used the calculation without the parenthesis at all, Jirka added parenthesis. Are they necessary or not?
00:41:32They are not.
00:41:33No, they are not necessary. That's correct. So let's try example C the third one.
00:41:37So we'll try Petra and Stepanka. Come on girls.
00:41:45So, for you I have: with the difference of numbers three and seven.
00:41:50May I write it with (inaudible)?
00:41:51To the difference of numbers three and seven we add the quotient of numbers five and eight.
00:42:03So, with the difference of numbers three and seven add the quotient of numbers five and eight.
00:42:10Petro there is the quotient of five and eight, do you have it there?
00:42:14Now she does.
00:42:15Now she does.
00:42:16Don't transcribe it into a fraction.
00:42:19You could write it in a fraction form for me. If it's possible do it that way.
00:42:30Into a fraction or into a mixed number?
00:42:33Into a fraction. Make it possible to have it in fraction form.
00:42:51Stepanko, look at the signs.
00:42:58So, Petro, are you checking signs?
00:43:03Minus four plus five eighths.
00:43:14So, Stepanko, minus four point zero is what?
00:43:22How many eighths?
00:43:28So, how many eighths?
00:43:31Four point zero?
00:43:34Four point zero. How many eighths is it?
00:43:42Four whole numbers! One whole number has how many eighths? Shh. Let's be patient a little longer.
00:43:49One whole number has how many eighths?
00:43:52And four of them?
00:43:54Is thirty-two.
00:43:55So it's minus thirty-two eighths plus five eighths is.
00:43:59Minus 28.
00:44:03Thirty-two without five?
00:44:06Twenty-seven eighths, so I have an assignment for you.
00:44:07The rest you finish by yourselves and the last example number six you'll do too. You'll write it down and calculate it.
00:44:14So the (inaudible).
00:44:18The last one? We'll go over the last one next time together. So, thank you and that's it.